Overview

This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers – both new and previously published – it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism. The author explores Brouwer’s idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer’s work. These figures includeMichael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting. This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics.

Full Product Details

Author:   Enrico Martino
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   Softcover reprint of the original 1st ed. 2018
Volume:   42
Dimensions:   Width: 15.50cm , Height: 1.00cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783030089719

ISBN 10:   3030089711
Pages:   170
Publication Date:   22 December 2018
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Brouwer, Dummett and the bar theorem.-  Creative subject and bar theorem.- Natural intuitionistic semantics and generalized Beth semantics.-  Connection between the principle of inductive evidence and the bar theorem.- On the Brouwerian concept of negative continuity.- Classical and intuitionistic semantical groundedness.- Brouwer’s equivalence between virtual and inextensible order.- An intuitionistic notion of hypothetical truth for which strong completeness intuitionistically holds.- Propositions and judgements in Martin-Löf.-  Negationless Intuitionism.- Temporal and atemporal truth in intuitionistic mathematics.-  Arbitrary reference in mathematical reasoning.-  The priority of arithmetical truth over arithmetical provability.- The impredicativity of the intuitionistic meaning of logical constants.- The intuitionistic meaning of logical constants and fallible models.

Reviews

Anyone with an interest in the murkier aspects of intuitionism will find this book well worth reading. (Peter Fletcher, Studia Logica, Vol. 107, 2019)

“Anyone with an interest in the murkier aspects of intuitionism will find this book well worth reading.” (Peter Fletcher, Studia Logica, Vol. 107, 2019)

Author Information

Enrico Martino was associated professor (now retired) of Logic and Philosophy of Mathematics in the department of Mathematics and, subsequently of FISPPA of the University of Padua. His main interests are Philosophy of Logic and Mathematics.  

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